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222-9+11+12:2*14+14 = ? ( )

Toán Lớp 6: Tính Tổng A.B.C A=1+2+3+…+100 B=1/1.2+1/2.3+…+1/99.100 C=(1-1/2)(1-1/3)(1-1/4)…(1-1/100)

Toán Lớp 6: Tính Tổng A.B.C
A=1+2+3+…+100
B=1/1.2+1/2.3+…+1/99.100
C=(1-1/2)(1-1/3)(1-1/4)…(1-1/100)

Comments ( 2 )

  1. A = 1 + 2 + 3 + …. + 100
    A = ( 100 +1 ) . 100 : 2
    A = 101 . 100 : 2
    A = 10100 : 2
    A = 5050
    ________________________________________
    B = 1/(1 . 2 ) + 1/( 2 . 3 ) + …. + 1/( 99 . 100 )
    B = 1/1 – 1/2 + 1/2 – 1/3 + …. + 1/99 – 1/100
    B = 1 – 1/100
    B = 99/100
    _________________________________________
    C = ( 1 – 1/2 ) . ( 1 – 1/3 ) . ( 1 – 1/4 ) …. ( 1 – 1/100 )
    C = 1/2 . 2/3 . 3/4 …. 99/100
    C = ( 1 . 2 . 3 …. 99 )/( 2 . 3 . 4 …. 100 )
    C = 1/100
    ⇒ A . B . C = 5050 . 99/100 . 1/100 = 9999/4

  2. Lời giải và giải thích chi tiết:
    A=1+2+3+…+100
    A=[(100+1).[(100-1):1+1]]/2
    A=[101.[99:1+1]]/2
    A=[101.[99+1]]/2
    A=[101.100]/2
    A=[101.50.2]/2
    A=101.50
    A=5050
    ________________________________________________________________
    B=1/1.2+1/2.3+…+1/99.100
    B=1-1/2+1/2-1/3+…+1/99-1/100
    B=1-1/100
    B=100/100-1/100
    B=99/100
    _______________________________________________________________________
    C=(1-1/2)(1-1/3)(1-1/4)…(1-1/100)
    C=(2/2-1/2)(3/3-1/3)(1-1/4)…(1-1/100)
    C=1/2. 2/3. 3/4…99/100
    C=1/100
    ________________________________________________________
    Ta có:tổng A.B.C
    =5050. 99/100. 1/100
    =5050. 99/200
    =9999/4

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222-9+11+12:2*14+14 = ? ( )